The neutrino matrix: why are there three of everything?

Last week’s results from the Daya Bay neutrino experiment were the first real measurement of the third neutrino mixing angle, θ13 (theta one-three). There have been previous experiments which set limits on the angle, but this is the first time it has been shown to be significantly different from zero.

Since θ13 is a fundamental parameter in the Standard Model of particle physics1, this would be an important measurement anyway. But there’s a bit more to it than that.

Neutrinos – whatever else they might be doing – mix up amongst themselves as they travel through space. This is a quantum mechanical effect, and comes from the fact that there are two ways of defining the three types of neutrino.

You can define them by the way they are produced. So a neutrino which is produced (or destroyed) in conjunction with an electron is an “electron neutrino”. If a muon is involved, it’s a “muon neutrino”. The third one is a “tau neutrino”. We call this the “flavour”.

Or you can define them by their masses. Usually we just call this definition neutrinos 1, 2 and 3.

The two definitions don’t line up, and there is a matrix which tells you how much of each “flavour” neutrino overlaps with each “mass” one. This is the neutrino mixing matrix. Inside this matrix in the standard model there are potentially four parameters describing how the neutrinos mix.

You could just have two-way mixing. For example, the flavour states might just mix up neutrino 1 and 2, and neutrino 2 and 3. This would be the case if the angle θ13 were zero. If it is bigger than zero (as Daya Bay have now shown) then neutrino 1 also mixes with neutrino 3. In this case, and only in this case, a fourth parameter is also allowed in the matrix. This fourth parameter (δ) is one we haven’t measured yet, but now we know it is there. And the really important thing is, if it is there, and also not zero, then it introduces an asymmetry between matter and antimatter.

This is important because currently we don’t know why there is more matter than antimatter around. We also don’t know why there are three copies of neutrinos (and indeed of each class of fundamental particle). But we know that three copies is minimum number which allows some difference in the way matter and antimatter experience the weak nuclear force. This is the kind of clue which sets off big klaxons in the minds of physicists: New physics hiding somewhere here! It strongly suggests that these two not-understood facts are connected by some bigger, better theory than the one we have.

We’ve already measured a matter-antimatter difference for quarks; a non-zero θ13 means there can be a difference for neutrinos too. More clues.

So not only did last week see the start of antimatter spectroscopy (which will check that there really is no matter-antimatter asymmetry in the electromagnetic force), it also saw the result which shows that experiments such as T2K in Japan and Nova in the US, which are looking for matter-antimatter asymmetry in the weak force, amongst neutrinos, are not wasting their time.

Unlike the ALPHA anti-hydrogen experiment at CERN, the Daya Bay people have put their result somewhere you can actually read it – thanks.

1 The “new” standard model, i.e. the one with massive neutrinos.

2 These choices of definition are called “eigenstates”; they are essentially different measurements of the neutrino wave-function. So you might in principle measure a neutrino such that you know it is 1,2 or 3, but then you don’t know what flavour it is until you measure that (similar to not knowing whether Schrödinger’s cat is alive or dead until you open the box). And once you’ve done that, you no longer know its mass. Quantum mechanics is great.